A Reconfigurable and Area-Efficient Polynomial Multiplier Using a Novel In-Place Constant-Geometry NTT/INTT and Conflict-Free Memory Mapping Scheme

Abstract

Out-of-place constant-geometry (CG) NTT usually has a simple and uniform memory access pattern. However, out-of-place CG NTT always requires ping-pong memory, resulting in a memory capacity requirement of $2N$ . Therefore, we propose a novel radix-4 in-place CG (IPCG) NTT/INTT that reduces the capacity requirement from $2N$ to N. An area-efficient and dynamical reconfigurable polynomial multiplier (RAEPM) based on IPCG NTT is proposed to speed up polynomial multiplication over rings. In RAEPM, a Barrett modular multiplier using area-efficient radix-4 booth multiplier is designed to reduce area. In addition, an odd-bank buffer structure is proposed to achieve conflict-free memory mapping independent of polynomial length N and NTT/INTT stage. Moreover, we also proposed an efficient modular reduction for specific numbers and introduced a division equivalent method to eliminate the odd number modular reduction and odd number division in addressing. RAEPM is implemented on Xilinx VC709 FPGA and runs at 294MHz clock frequency. Compared with the prior pure NTT accelerators, under the same parameters, RAEPM achieves a decrease of 39.02% $\sim ~57.63$ % in area-time complexity of equivalent LUT, and a decrease of 15.97% $\sim ~49.24$ % in area-time complexity of equivalent FF. Compared with the prior NTT-based polynomial multipliers, under the same parameters, RAEPM achieves a decrease of 35.48% $\sim ~90.81$ % in area-time complexity of equivalent LUT, and a decrease of 24.24% $\sim ~88.41$ % in area-time complexity of equivalent FF.